QUESTION STEM:A regular hexagon has six equal sides, each of length 27.The perimeter of a polygon is the sum of...

1. TRANSLATE the problem information

• Given information:
  • Regular hexagon (6 equal sides)
  • Each side length = 27
  • Need to find perimeter
• What this tells us: We need to add up 6 sides, each with length 27

2. TRANSLATE the perimeter concept

• Perimeter = sum of all side lengths
• For equal sides: Perimeter = number of sides × length of each side
• For this hexagon: \(\mathrm{Perimeter = 6 \times 27}\)

3. SIMPLIFY the calculation

• Calculate: \(\mathrm{6 \times 27 = 162}\)
• You can verify: \(\mathrm{6 \times 20 + 6 \times 7 = 120 + 42 = 162}\)

Answer: 162

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may forget that a hexagon has 6 sides and use the wrong number of sides in their calculation.

They might think a hexagon has 5 sides (confusing with pentagon) or 8 sides (confusing with octagon), leading to calculations like \(\mathrm{5 \times 27 = 135}\) or \(\mathrm{8 \times 27 = 216}\). This causes them to get stuck or provide an incorrect answer.

Second Most Common Error:

Poor SIMPLIFY execution: Students understand the setup correctly but make an arithmetic error when calculating \(\mathrm{6 \times 27}\).

Common mistakes include \(\mathrm{6 \times 27 = 152}\) or \(\mathrm{6 \times 27 = 172}\), leading to incorrect final answers due to computational errors rather than conceptual misunderstanding.

The Bottom Line:

This problem tests whether students can correctly identify the number of sides in a hexagon and apply the basic perimeter formula. The key insight is that "regular" means all sides are equal, so multiplication can replace repeated addition.